Solve for $x$ : $ 6|x - 7| + 9 = 2|x - 7| + 2 $
Subtract $ {2|x - 7|} $ from both sides: $ \begin{eqnarray} 6|x - 7| + 9 &=& 2|x - 7| + 2 \\ \\ { - 2|x - 7|} && { - 2|x - 7|} \\ \\ 4|x - 7| + 9 &=& 2 \end{eqnarray} $ Subtract ${9}$ from both sides: $ \begin{eqnarray} 4|x - 7| + 9 &=& 2 \\ \\ { - 9} &=& { - 9} \\ \\ 4|x - 7| &=& -7 \end{eqnarray} $ Divide both sides by ${4}$ $ \dfrac{4|x - 7|} {{4}} = \dfrac{-7} {{4}} $ Simplify: $ |x - 7| = -\dfrac{7}{4}$ The absolute value cannot be negative. Therefore, there is no solution.